Results from molecular dynamics experiments pertaining to the encapsulation of ClO4- within the hydrophobic cavity of an aqueous alpha-cyclodextrin (alpha-CD) are presented. Using a biased sampling procedure, we constructed the Gibbs free energy profile associated with the complexation process. The profile presents a global minimum at the vicinity of the primary hydroxyl groups, where the ion remains tightly coordinated to four water molecules via hydrogen bonds. Our estimate for the global free energy of encapsulation yields Delta G(ene) similar to -2.5 k(B)T. The decomposition of the average forces acting on the trapped ion reveals that the encapsulation is controlled by Coulomb interactions between the ion and OH groups in the CD, with a much smaller contribution from the solvent molecules. Changes in the previous results, arising from the partial methylation of the host CD and modifications in the charge distribution of the guest molecule are also discussed. The global picture that emerges from our results suggests that the stability of the ClO4- encapsulation involves not only the individual ion but also its first solvation shell.